SQL Row_Number() function is to sort and assign an order number to data rows in related record set. So it is used to number rows, for example to identify the top 10 rows which have the highest order amount or identify the order of each customer which is the highest amount, etc.
If you want to sort the dataset and number each row by seperating them into categories we use Row_Number() with Partition By clause. For example, sorting orders of each customer within itself where the dataset contains all orders, etc.
SELECT
SalesOrderNumber,
CustomerId,
SubTotal,
ROW_NUMBER() OVER (PARTITION BY CustomerId ORDER BY SubTotal DESC) rn
FROM Sales.SalesOrderHeader
But as I understand you want to calculate the number of rows of grouped by a column. To visualize the requirement, if you want to see the count of all orders of the related customer as a seperate column besides order info, you can use COUNT() aggregation function with Partition By clause
For example,
SELECT
SalesOrderNumber,
CustomerId,
COUNT(*) OVER (PARTITION BY CustomerId) CustomerOrderCount
FROM Sales.SalesOrderHeader